Real‐time dose reconstruction for wedged photon beams: a generalized procedure

A practical and accurate generalized procedure to reconstruct the isocenter dose Diso for 3D conformal radiotherapy (3DCRT) has been developed for X‐ray open beams supplied by linacs of different manufacturers and equipped with aSi electronic portal imaging devices (aSi EPIDs). This paper reports an extension of the method, to be applied at the wedged X‐ray beams characterized by the wedge attenuation factor WAF. Using water‐equivalent solid phantoms (SPs) of different thicknesses, w, and photon square fields of sizes, L, the generalized midplane doses D0(WAF,w/2,L) and generalized transit signals st0(WAF,w,L) by 38 beams of six different linacs were determined. The generalized data were fitted by surface equations and used together with the information of the ‘record & verify’ network of the centers. In this manner, for every beam, the Diso reconstruction was obtained in about 25 seconds after the treatment. To test the in vivo dosimetric procedure, six pelvic treatments that used conformed wedged beams were carried out with three linacs of different manufacturers. For every beam, the comparison between the reconstructed Diso and the Diso,TPS computed by the TPS, resulted in an acceptable tolerance level of ±5%, estimated for this kind of treatment. Generally the in vivo dosimetry methods that use EPIDs require: (i) a special effort for the dosimetric commissioning with SPs of different thicknesses, and (ii) extra time for the analysis of the EPID signals. The proposed procedure simplifies the commissioning step and supplies for Varian, Elekta, and Siemens linacs equipped with the aSi EPIDs a quasi‐real time in vivo dosimetry for open and wedged 3DCRT fields. PACS number: 87.53Xd

particular, the in vivo dosimetry could discover the discrepancies between the reconstructed and the expected doses due to pretreatment and intreatment errors. The in vivodoseverification is actually one of the major concerns in radiotherapy, and we believe it will become mandatory in many countries in the future. (2) Some researchers have demonstrated the advantages of reconstructing the delivered dose during the treatment using a 2D array as the amorphous silicon electronic portal imaging device (aSi EPID). (3) The present authors have developed an in vivo dosimetry method for the 3D conformed radiotherapy technique (3DCRT) for open beams based on the ratios between the transit signals measured by aSi EPIDs, and the midplane doses of a water-equivalent solid phantom (SP). (4) The method has been applied to test head, thorax, pelvic, and breast tumors in radiotherapy treatments. (4,5) However all the procedures based on the transit signals by the EPIDs (6,7,8) requirespecific measurements with SPs for every beam. Recently, the authors have developed a generalized procedure for the in vivo dosimetric reconstruction at the isocenter point of the 3DCRT that used open photon beams of different linacs characterized by the TPR 20,10 quality index (herein named TPR). The method can be easily commissioned for linacs manufactured by Varian, Elekta, and Siemens and equipped with aSi EPIDs (9) reducing the measurements with SPs.
The aim of this work was the implementation of the generalized procedure for the 3DCRT wedged beams characterized by the wedge attenuation factor, W AF . A dedicated software that uses the 'record and verify' (R&V) network of the center supplied the in vivo dosimetry tests in quasi-real time. Table 1 reports same geometric and dosimetric characteristics of the 38 wedged X-ray beams examined.Thebeamsof6,10,and15MVweresuppliedbysixlinacsoperatinginfive centers:

A. Wedged beams
• twoClinacVarianlinacs(VarianMedicalSystem,CA),onesupplying6MVand10MV and one supplying 6 MV and 15 MV • twoElektaPreciselinacs(Elekta,Stockholm,Sweden)supplying6,10and15MV • twoOncorSiemens(SiemensA.G.Erlangen,Germany)onesupplying6MV,and10MV and one supplying 6MV and 15 MV The linacs were equipped with aSi EPIDs, based on panels of aSi sensors operating as a two-dimensional photodiode array. A more detailed description of the functionality and basic properties of such devices is reported in the literature. (10,11) The EPIDs included a metal plate that provides some buildup for the photons, and absorbs enough low energy scattered radiation that reduces image quality. A common source-EPID metal plate distance (SED) equal to 159 cm was used in this work for every linac. The linacs were equipped with multileaf collimators and the X-ray beams have been calibrated in water-phantom following the IAEA protocol. (12) Figure1showsthecentralsectionsofthewedgefilterssuppliedbythethreemanufactures for their linacs.
The wedged beams were characterized by the wedge attenuation factor (13) W AF , defined for a reference beam 10 × 10 cm 2 at the SAD as the ratio between the doses obtained by an  supplied by Varian for 15°, 30°, 45°, and 60°, by Siemens for 15°, 30°,  45°, and 60°, and by Elekta for 60°. ion chamber at the reference depth d ref =10 cm in water phantom, measured with the filter (Fig. 2(a)) D SAD,W andwithoutfilterD SAD,0 ( Fig. 2(b)). (1) Generally this factor is obtained during the commissioning measurements in water phantom. However, in this work the index TPR (12) for each wedge beam was also measured. Table 2 reports some parameters that characterize the wedged beams supplied by (a) Varian, (b) Siemens, and (c) Elekta linacs. In particular, as a function of the nominal potential MV Table2reports,thewedgeangles(definedastheanglebetweenthebeamcentralaxisandthe isodose direction at the d ref ,thethickness,t,ofthefilteredmaterialonthebeamcentralaxis, W AF , and the TPR indexes for open and wedged beams. In previous papers, (14)(15)(16) the quality index TPR resulted a good parameter to select the generalized dose at midplane phantom and the transit signals. Indeed, these data showed for everycoupleofphantomthicknesses,w,andphotonsquarefieldside,L,aproportionaltrend asafunctionoftheTPR.ThepresenceofthewedgedfiltersforbeamsofthesameMVreduces the soft radiation component and TPR values for open and wedged beams changed within 4%,1.5%,and0.7%for6,10,and15MVbeams,respectively,confirmingliteraturedata. (17) However,theTPRvaluesfor15°and60°filterschangewithin2.5%,1.0%,and0.5%for6, 10, and 15 MV beams, respectively. It is important to underline that the TPR indexes are obtained as the ratios between the doses (at distance of 100 cm from the source) at depth 20 cm (D 20 ) and 10 cm (D 10 ) for open beams 10 × 10cm 2 indicating the different beam hardness. Forwedgedbeams,thefiltershapes( Fig.1)areprojectedtoobtainmodulatedfluencewitha minimum variation of the percentage depth dose along the beam central axis. In particular, the TPRindexforwedgedbeamstakesintoaccountthehardeningandthespatialphotonfluence modulation,loosingtheproportionaltrendwithfilterthickness,t.Inthisregard,TPRsforthe wedged beams did not correlate with the dose at the mid plane phantom and the transit signals. The index W AF changes about 180% for the different wedge angles (Table 2), and it is well correlated with the doses and transit signals. For this reason the W AF was selected in this work to characterize the wedge beams.

B. Isocenter dose reconstruction method
The method used for the dose reconstruction at the isocenter point D iso has been described in previous papers for open beams. (14)(15)(16) Following that approach, correlation ratios between the transit signals, measured by an aSi EPID at the SED, positioned below an SP of thickness, w, and the dose values at the SP midplane along the beam central axis at the SAD ( Fig. 2(c)) were determined for each beam of the same MV. In particular, for the wedged X-ray beams of square fieldsizeL,specificcorrelationratios were determined by: ( where are the transit signals and the is the midplane dose in SP. Moreover, a set of measurements were carried out positioning the phantom midplane (at distances d up to ± 7 cm) below and above the SAD. This produced the different scattered photon contributions on the EPID due to the different distances between the portal detector and the bottom surface of the phantom that were taken into account by the ratios: These ratios also take into account the eventual changes of beam hardening due to the presence of the patient along the beam central axis that can be responsible for an aSi detector reading dependence.

B.1 Midplane doses by wedged fields
The SP, an RMI model 457 (Gammex, RMI Middelton, WI) with 30 cm square slabs of various thicknesses, presented a density of 1.045 ± 0.005 g/cm 3 . A water equivalency correction factor, k E (18) for the SP resulted equal to k E = 1.011 (14) so the ion chamber reading in SP was multiplied by the k E before the midplane dose determination.
However, MU calibrations were carried out in the centers using different source waterphantom surface distances (SSD) or different dose values at the reference depth, d ref = 10 cm in water phantom. In particular, using an open 10 × 10 cm 2 fieldattheSSD,areferenceoutput factor of 1 cGy/MU was assigned at the depth of the maximum dose, d max , for the Varian and Siemens linacs, while for the Elekta linacs the reference output factor was assigned at d ref .
For this reason, a factor k 0 hasbeendefinedas (4) In this way, the midplane doses were normalized by the factor k 0 (5) thus obtaining a set of generalized dose values in terms of cGy/MU that were independent of the MU calibration adopted by the centers.

B.2 EPID calibration and transit signal measurements
TheEPIDimageswereexportedasDigitalImagingCommunicationinMedicine(DICOM)files to be analyzed. Some characteristics of the aSi EPIDs and their running acquisition modes have been well reported in previous works for the open beams (14)(15)(16) where the EPID signal, s, on the beam central axis in terms of arbitrary units (a.u.) was obtained by the average of the signals supplied by a number of central pixels around the beam's central axis for a 4 × 4 mm 2 area.
It is well known that aSi EPIDs present a nonlinearity response with the treatment exposure times due to the combination of the 'image lag' and the 'gain ghosting' effects. As reported by Mc Dermott et al., (10) to assess the linearity response of the different aSi EPIDs, the signals were measured delivering a number, N, of MUs equal to 5, 20, 50, 100, 200, 300, and 400 MU. A correction factor for the linearity, k lin , was determined for each clinical MU rate utilized (Table 1), as (6) where s and s N were the signals obtained for 100 and N MU, respectively. Moreover, the signal dependence on the dose rate was analyzed by the k lin factors, obtained irradiating SPs with different thickness, w = 10, 22, 30, 42 cm (Fig. 2(c)).
The EPIDs were calibrated determining a reference transit signal, s r,t , (in terms of arbitrary unitsa.u.)intheconfigurationreportedinFig.2(c).Inparticular,theSPwithathicknessw= 22cmwasirradiatedbyafield10× 10 cm 2 , with 100 MU and the s r,t value in a.u./MU was converted to one centi-calibration unit per MU (1 cCU/MU). This way 38 sensitivity factors, k s , in terms of cCU/a.u were determined for every EPID and wedged beam by: Thus,irradiatingtheSPofdifferentthicknesses,w,withwedgebeamsoffieldsizes,L, the transit signals in a.u./MU were multiplied by the k s factors, obtaining the generalized transit signals (8) The values in terms of cCU/MU resulted independently from the MU calibra-tionandtheaSiEPIDsensitivity.Ofcourse,anintegraltransitsignal,s t (a.u.) (obtained by a number of MUs) multiplied by k s can be read in terms of cCU and resulted independent from the EPID sensitivity and the MU calibration.
The measurements of the were also carried out, positioning the phantom midplane below and above the SAD (at distances, d, up to ±7cm)asafunctionofw,andL.These last data were used to determine the generalized ratios, ,definedbyEq.(3).

B.3 An interactive software for the generalized dose reconstruction
Using a commercial software package, TableCurve 3D, SPSS-Science2000 (Systat Software, Inc., San Jose, CA), (19) thedatareportedbyEqs. (5)and (8)wereanalyzedandfittedbysurface equations.Thesoftwarepackageautomatesthesurface-fittingprocessminimizingthesumof squares of the residuals (where a residual is simply the difference between the experimental valueandtheonecomputedfromthesurface-fitequation). (20) This way, the surface equations for the and the experimental data can be used to obtain generalized correlation ratios (in terms of CU/Gy, Eq. (2)).
The second module of the DISO is for the 'posttreatment step'.The DICOM files from the EPID after the patient's daily treatment have been analyzed to determine, for every beam, the D iso value, as well as the ratio R = D iso /D iso,TPS . In particular, for every beam, the images of the isocenter CT scan with the beam geometrical edges and the central axis direction have been reported.
A preliminary test to verify the accuracy of the generalized procedure was obtained following 12 radiotherapy treatments of prostatic tumors, four cases for each of the three linacs (Varian, Elekta, and Siemens) (not included in Table 1). This meant that the factors k 0 , k s , k lin and W AF of the new linacs were determined. The selection of these pelvic treatments assured a good accuracy in terms of: (i) the D iso,TPS computation in quasi-homogeneous tissues, and (ii) the patient setup. For each patient, six tests were carried out for a total of 144 tests for wedge beams of 10 and 15 MV used for the later-lateral irradiations. In particular, the 15 MV Siemens beams used 30° and 45° wedges, while the 10 MV Varian beams used a 30° wedge, and the 10 MV Elekta beams used the 60° wedge.
The TPSs used for the MU computations to deliver the D iso,TPS were two 3D Eclipse (Eclipse 7.3.10Varian,PaloAltoCA,USA)andone3.0OncentraMasterplan(NucletronBV,Venendal, The Netherlands) in the center that used the Elekta linac.
The aim of these 144 tests was to verify the ratios, R, obtained by the generalized procedure and that were within the tolerance level 5%, estimated for this treatment. Table 3 reports the factors k 0 and k s determined for 15 of the 38 wedged beams. The W AF longterm stability was estimated equal to ± 0.3% -that means within the experimental uncertainty. A long-term stability for the s r,t was equal to 2% (2 SD). This means that when the s r,t changes in time over this tolerance level, a new k s factor should be adopted to take into account the change of the EPID sensitivity.

A. Midplane doses and transit signals
The k lin factors for the same EPID model resulted within ± 0.5% independent of the nominal MV and the dose rate, in agreement with the data reported by McDermott et al. (10) Table 4 reports the average values of the k lin factors determined for the aSi EPID models here used (Table 1).
Figure3reportsthelinearfitsofthegeneralizedtransitsignals for 10 × 10 cm 2 fieldsofthesameMVasafunctionoftheW AF and for phantom thicknesses w = 10, 22,and42cm.Thefitsreproducethemeasureddata,wellwithintheexperimentaluncertainties ± 2.5% (2SD) estimated for these data, and the same accuracy was obtained for the other fieldsizes. Figure3showsthatthegeneralizedsignalsforw=22cmareequaltotheunityfor  alltheMVbeams(Eq.(8)).Ofcourse,increasingordecreasingthephantomthicknessw,data result, respectively, less or greater than the unity and, in particular, the changes from the unity increase for beams of minor MV values. As reported in Table 2, the poor variations of the TPRs  for wedged beams of the same MV, (in particular, for 10 MV and 15 MV) is coherent with the small variations of the relative photon transmissions given by Eq. (8). For example, the heavy line for 15 MVs reported in Fig. 3 for the w = 42 cm is obtained by the ratios (9) and for different W AF values, these ratios are constant enough, while for the beams of 6 MV, the ratios change for the different wedges.
Similar trends as from Fig. 3 were obtained for the midplane dose andthelinearfitsreproducedtheexperimentaldatawellwithintheexperimentaluncertainty± 2% (2SD) estimated for the generalized doses. In conclusion, for every MV, the experimental doses (Eq.(5))werefittedbysurfaceequationsonceforeverysquare fieldLby: wherethesixadjustablecoefficients,a i (i=1,..,6),arerealnumbersobtainedthroughthefitting procedure. The number of adjustable parameters (10 and 6 in Eqs. (10) and (11)) were chosen to obtain the computed data within the uncertainties of the experimental data estimated for the midplane doses and the transit signals.
The resulted independently from the W AF (within 0.3%).

B. Isocenter dose determination
Following in part the approach used for open beams, (9) the dose D iso for a generic wedged beam has been obtained by: (13) where in terms of a.u. is the EPID integral signal that is corrected by: (i) the sensitivity factor k s to take into account for the EPID sensitivity, (ii) by the k 0 factor to take into account for the MU calibration, and (iii) by the factor k lin , to take into account for the nonlinearity of the EPID signal with the MUs. In square brackets, Eq. (13) reports, for every MV, the correlationratio(Eq.(12)),thef(w,L,d) MV factors and the tissue maximum ratios . (21) In particular, by the W AF beam index and the patient's radiological thickness w (Eqs. (10) and (11)), supplied the data for the ratio F 0 (W AF ,w,L),whilethef(w,L,d) MV and the ratios were selected by interpolations of tabulated data for each MV parameter. The dosimetric accuracy of the method was analyzed in a previous paper (4) and, in particular, for the ratio, R, between the in vivo reconstructed dose D iso and the predicted dose, D iso,TPS , a tolerance level of 5% was assumed. (5) Figure 6 reports the histogram of 131 tests over the 144 carried out for six pelvic treatments. In fact, 13 tests on three patients showed dose overestimations between 8% and 12% due to the presence of air pockets along the beam central axis, and these results were not reported in Fig.6.Intheselasttests,thetransitsignalprofilesthatcrossedthebeamcentralaxisshowed small localized increases if compared with other previous controls. The visual portal imaging (VPIs)obtainedbeforethetreatmentconfirmedthepresenceofgaspockets.However,forevery patient, the sum of doses (obtained by the beams reported in Fig. 6) were well within 4% of the stated doses, D iso,TPS .Figure6confirmedtheratios,R,wellwithinthetolerancelevelof5% estimated for each test of the 3DCRT pelvic treatment. Moreover, the generalized procedure thatadoptsanewsoftwarefortheDISO,suppliedtheD iso reconstructions after 1.5 minutes at the end of a treatment with four beams.

IV. dIScuSSIon
The dosimetric procedure for the in vivo dosimetry here reported is based on the use of generalized functions and obtainedfittingtheexperimentaldataof38wedgedbeamsof linacsofdifferentmanufacturers.OriginalcalibrationprocedureswereadoptedfortheD 0 (W AF , w/2,L)(Eq.(5))thatresultedindependentlyoftheMUcalibrationadoptedbythecentersand the (Eq. (8)) that resulted independent of both the EPID sensitivity and the MU calibration of the beams.
The linacs, as the EPIDs manufactured by Varian, Elekta, and Siemens, present a different collimatorandwedgefilterassemblage (22,23) (different distances from the source), as well as different EPID-building. (8,24,11) This can be a cause of different scatter photon contributions by collimators, wedges, and by the EPID itself. However, the effect of the different photon scattered contributions from the collimators and the wedges as a function of the beam size seems tobenegligible,andisbasedonthelowresidualsforthefitsofEq. (11).Inotherwords,the generalized seems to be independent of linac type. Moreover, the low residuals by Eq. (10) suggested that the effects of different backscatter contributions from the EPIDsofdifferentmanufacturerswerenegligiblefortheSPthicknessesandfieldsizeshere used. In other words, the generalized values seemed to be independent of linac type.
The time required for the measurements with the SPs for the correlation ratios (Eq. (2)) and the ratios of Eq. (3) were estimated to be six hours per open and wedged beams of the same MV. Using the generalized functions, the measurements to be carried out in the centers were reduced to those for the determination of the W AF , k 0 , k s , and k lin parameters.Wehaveverified that in 2 hours it is possible to determine the four parameters for all the linac beams. In particular, Eq. (7) supplies the k s factors obtained with w = 22 cm of SP. At the moment, we have determined for each beam of the different linacs, the ratios between k s and k s,0 . The latter was obtained in the same manner but in the absence of the SP. In this way, the k s stability could be tested every month, determining the k s,0 .
The extra time needed for the pretreatment step resulted in about 40 sec per beam, while for the post-treatment step, it resulted about 25 sec per beam.

V. concLuSIonS
In vivo dosimetry is today considered a special tool to avoid accidents, (2) and many researchers are studying new methods based on the use of EPIDs that are easy to implement, simple, efficientintheirdailyuse,andsufficientlyaccurateforthepurposetheyareserving. (25) Recent methodsbasedontransitdosimetryrequirespecificmeasurementsinphantom (10,7,4) and data analysis after the treatment. This paper extends a generalized procedure developed for open beams at the 3DCRT wedged beams supplied by linacs manufactured by Varian, Elekta, and Siemens. This way, the implementation measurements in solid water phantoms can be strongly reduced and the method can be easily included in the QA program (26) of the centers. Moreover, thededicatedsoftwareDISOsuppliesanaccurateD iso reconstruction at the end of the fractioned therapy in quasi-real time.
The method based on the correction functions can be applied for breast treatment (27) using measurements in cylindrical water phantoms. This means that new generalized functions could be determined for this technique.
At the moment, the authors are studying the possibility of extending the generalized procedure for the D iso reconstruction for intensity-modulated radiotherapy beams, in particular for a 2D in vivo dose investigation.